TY - JOUR
A2 - Rassias, John
AU - Gordji, M. Eshaghi
AU - Khodaei, H.
PY - 2010
DA - 2010/09/27
TI - The Fixed Point Method for Fuzzy Approximation of a Functional Equation Associated with Inner Product Spaces
SP - 140767
VL - 2010
AB - Th. M. Rassias (1984) proved that the norm defined over a real vector space X is induced by an inner product if and only if for a fixed integer n≥2, ∑i=1n∥xi-(1/n)∑j=1nxj∥2=∑i=1n∥xi∥2-n∥(1/n)∑i=1nxi∥2 holds for all x1,…,xn∈X. The aim of this paper is to extend the applications of the fixed point alternative method to provide a fuzzy stability for the functional equation ∑i=1nf(xi-(1/n)∑j=1nxj)=∑i=1nf(xi)-nf((1/n)∑i=1nxi) which is said to be a functional equation associated with inner product spaces.
SN - 1026-0226
UR - https://doi.org/10.1155/2010/140767
DO - 10.1155/2010/140767
JF - Discrete Dynamics in Nature and Society
PB - Hindawi Publishing Corporation
KW -
ER -